In a lithography process to manufacture electronic devices (microdevices) such as liquid crystal display devices, semiconductor devices and the like, a projection exposure apparatus of a step-and-repeat method (a so-called stepper), a projection exposure apparatus of a step-and-scan method (so-called scanning stepper (also called a scanner)) and the like are mainly used. As for an exposure apparatus for manufacturing liquid crystal display devices (a liquid crystal exposure apparatus), according to an increase in substrate size, a scanning type projection exposure apparatus such as a scanner has become mainstream.
Electronic devices (microdevices) are manufactured by overlaying and forming a pattern of a plurality of layers on a substrate (a glass plate, a wafer and the like). Therefore, in an exposure apparatus, it is necessary to accurately overlay and transfer a mask pattern onto a pattern which is already formed in each shot area on the substrate, that is, high overlay accuracy is required.
In order to achieve high overlay accuracy, a technique of precisely and stably driving a substrate stage which moves holding a substrate becomes necessary. Here, in recent years, as the substrate stage, a gantry stage is mainly employed which is equipped with a carriage which moves in a scanning direction of the substrate at the time of scanning exposure, and a substrate table which is supported on the carriage and moves in a non-scanning direction while holding the substrate. The gantry stage and the like generates resonance which may become an obstacle factor when driving the substrate stage stably with high precision. Especially recently, with the size of the substrate stage increasing, the resonance frequency (natural frequency) is becoming lower.
As a theoretical framework for structuring a robust control system with respect to high bandwidth including a resonance band of such a substrate stage and also to variation of resonance frequency using a notch filter, a stage controller is known which utilizes an advanced robust control theory represented by the H-infinity control theory (for example, refer to Patent Literature (PTL) 1). In the advanced robust control theory, while a sensor is added so as to make the plant a system of one input and multiple outputs, there are no restrictions to the placement of the added sensor, and further, a feedback controller can be designed which is also stable to a modeling error of a nominal model. However, in general, because degrees of freedom in designing a controller increases according to a structure of the plant, an order of a weight function and the like, a trade-off relation occurs between the high bandwidth and the robustness of the feedback controller.